Problem: What's the first wrong statement in the proof below that $ \triangle BDE \cong \triangle BCE$ $ \; ?$ $ \overline{BC} $ is parallel to $ \overline{DF} $. This diagram is not drawn to scale. $A$ $B$ $C$ $D$ $E$ $F$ Givens $ \overline{EF} \cong \overline{BE}$ $, \ $ $ \angle CEF \cong \angle BED$ $, \ $ $ \angle ECF \cong \angle BDE$ $, \ $ $ \angle ABC \cong \angle DBE$ $, \ $ $ \overline{AB} \cong \overline{BE}$ $, \ $ and $\ $ $ \angle BAC \cong \angle BED$ Proof $ \triangle BDE \cong \triangle FCE$ because AAS $ \overline{DE} \cong \overline{CE}$ because corresponding parts of congruent triangles are congruent $ \overline{DF} \cong \overline{AB}$ because corresponding parts of congruent triangles are congruent $ \angle BED \cong \angle CBE$ because alternate interior angles are equal $ \angle DBE \cong \angle CFE$ because corresponding parts of congruent triangles are congruent $ \triangle BDE \cong \triangle BCE$ because SSS
Try going through the proof yourself: write down the givens, and then see if they justify the next step for the reason given. Then do the same thing for the next step, and the next, until you run into something that you can't justify, or you finish the proof. $ \overline{AB} \cong \overline{DF}$ is the first wrong statement.